The given equation is, x5+15x4+94x3+305x2+507x+353=0 If all the roots is increased by k, then (x−k)5+15(x−k)4+94(x−k)3+305(x−k)2+507(x−k)+353=0 …… (1) The value of k is calculated as, x4=−5k+15 −5k+15=0 k=3 Substitute the value in equation (1), (x−3)5+15(x−3)4+94(x−3)3+305(x−3)2+507(x−3)+353=0 The coefficient of x is, x=[5C4(−3)4+15(4C3(−3)3)+94(3C2(−3)2)+305(2C1(−3))+507] =5(81)+15(4)(−27)+94(3)(9)+305(2)(3)+507 =405−1620+2538−1830+507 =0